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The rationality of holomorphic Eisenstein series. (English) Zbl 0452.10031


MSC:

11F27 Theta series; Weil representation; theta correspondences

Citations:

Zbl 0155.404
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References:

[1] Andrianov, A.N.: The multiplicative arithmetic of Siegel modular forms, Russian Math. Surveys34, 75-148 (1979) · Zbl 0427.10017
[2] Andrianov, A.N., Kalinin, V.L.: On the analytic properties of standard zeta-functions of Siegel modular forms, Math. U.S.S.R. Sb.35, 1-18 (1979) · Zbl 0417.10024
[3] Baily, W.L., Jr.: Eisenstein series on tube domains, In: Problems in Analysis: A Symposium in Honor of Salomon Bochner, pp. 139-156, Princeton: Princeton University Press 1970 · Zbl 0211.10603
[4] Baily, W.L., Jr.: On the Fourier coefficients of certain Eisenstein series on the adèle group, In: Number Theory, Algebraic Geometry, and Commutative Algebra: in Honor of Y. Akizuki, Tokyo: Kinokuniya 1973
[5] Deligne, P.: Formes modulaires et représentationsl-adiques, Sém Bourbaki 68/69 No. 355, Lecture Notes in Mathematics179, 136-172 (1971)
[6] Garrett, P.B.: Pullback of Eisenstein Series; Applications, preprint
[7] Harris, M.: Special values of zeta functions attached to Siegel modular forms, preprint · Zbl 0465.10022
[8] Karel, M.: Eisenstein series and fields of defintion, Compositio Math.37, 121-169 (1978) · Zbl 0399.10027
[9] Klingen, H.: Zum Darstellungssatz für Siegelsche Modulformen, Math. Z.102, 30-43 (1967) Berichtigung. Math. Z.105, 399-400 (1968) · Zbl 0155.40401
[10] Raghavan, S.: Modular forms of degreen and representations by quadratic forms, Ann. of Math.70, 446-477 (1959) · Zbl 0093.08002
[11] Satake, I.: Theory of spherical functions on reductive algebraic groups overp-adic fields. Publ. Math. I.H.E.S.18, 1-69 (1963)
[12] Shimura, G.: On the Fourier coefficients of modular forms of several variables, Göttinger Nachr. Akad. Wiss. Nr. 17, 261-268 (1975) · Zbl 0332.32024
[13] Shimura, G.: The arithmetic of automorphic forms with respect to a unitary group, Ann. of Math.107, 569-605 (1978) · Zbl 0409.10016
[14] Siegel, C.L.: Einführung in die Theorie der Modulfunktionenn-ten Grades, Math. Ann.116, 617-657 (1939) · JFM 65.0357.01
[15] Tsao, L.-C.: The rationality of the Fourier coefficients of certain Eisenstein series on tube domains. Compositio Math.32, 225-291 (1976) · Zbl 0346.10014
[16] Zharkovskaya, N.A.: The Siegel operator and Hecke operators, Funct. Anal. Appl.8, 113-120 (1974) · Zbl 0314.10021
[17] Shimura, G.: On some arithmetic properties of modular forms of one and several variables. Ann. of Math.102, 491-515 (1975) · Zbl 0327.10028
[18] Shimura, G.: Theta functions with complex multiplication, Duke Math. J.43, 673-696 (1976) · Zbl 0371.14022
[19] Harris, M.: Rationality properties of automorphic forms, preprint (1981)
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